...we should not just adhere to the rhetoric historical elites used to justify their domination when we seek to accurately understand how a society functions.
When we study and evaluate ancient societies and seek to understand the manner in which they functioned, we have an obligation to do so skeptically and critically; we should not approach these societies on their own terms (or, rather, on their elites' own terms), but should instead evaluate whether or not they fit objectively-defined criteria when describing them.
A very clear, objective standard for "democracy" is "universal adult suffrage."
Calling Athenian democracy "democracy" with an understanding that in that time suffrage was very limited isn't "adhering to rhetoric," it's an accurate description of how an ancient society functioned. You're not being skeptical and critical, you're projecting our definitions and understandings of today to people of 2000+ years ago.
Your "clear, objective standard" has only been around within the last century or so (within this country) as compared to 2000+ years of a limited franchise. Maybe our definition - which I agree is the superior one - is the one that needs a new word or a modifier; "universal democracy" maybe. Or, perhaps, we should accept that definitions have changed over the centuries, as language, law and societies tend to do.